Hello, I am completely lost with this problem. Any guidance is greatly appreciated.
Let , let be the -field of Borel subsets of and let be the Lebesgue measure on . Let .
a. Starting from the fact that , show that , where is the collection of two-dimensional bounded rectangles of the form with , and
b. Let and be the inner and outer measures defined from . Prove that . (Hint: one way to do this is to construct sequences of sets and of known measure , e.g. unions of disjoint rectangles, with and )
Thanks in advance